Five5

five theories of illusion or erroneous perception –

Ātmakhyāti (Yogacara theory of subjective apprehension),
Asatkhyāti (Madhyamaka theory of the nonexistent),
Akhyāti (Prabhākara’s theory of non-apprehension),
Anyathākhyati (Nyaya theory of misapprehension) and
Anirvacanīyakhyāti (Advaita Vedanta theory of apprehension of the indeterminate), developed by five schools of thought

https://www.google.com/search?q=five+theories+of+illusion

Face

The five faces of Gayatri represent

Five Vital Forces:
They represent the five vital life forces or prāṇas that sustain life: prana, apana, vyana, udana, and samana.

Five Goddesses:

Each face can also be seen as a manifestation of different goddesses: Bhur, Saraswati, Lakshmi, Parvati, and Akash.

Five Directions:

The five faces also reflect her omnipresence by representing the five directions.

Five Colors:

In some depictions, the faces are shown in different colors: pearl (Mukta), coral (Vidruma), gold (Hema), blue (Neela), and white (Dhavala).

Five Elements: The faces represent the Pancha Bhutas, the fundamental elements from which

universe and the human body are made: Earth (Prithvi), Water (Jal/Apas), Fire (Agni/Tejas), Air (Vayu), and Ether/Space (Akash).

Five Sheaths : The five faces also correspond to the five sheaths (Pancha Koshas) of the human soul: the physical (anna-maya), vital energy (prana-maya), mental (mano-maya), intellectual (vijnana-maya), and bliss (ananda-maya) bodies.

Parts of the Mantra : In another interpretation, the five faces correspond to the five parts or clauses of the Gayatri Mantra:Om; Bhur Bhuvah Suvah; Tat Savitur Varenyam; Bhargo Devasya Dheemahi; and Dhiyo Yo Nah Prachodayat.